KIAN SHAEN V VILLANUEVA
PROBLEM SET 3
CE2-3
1.
TWO PEG TEST. IN THE TWO-PEG TEST OF A DUMPY LEVEL THE FOLLOWING OBSERVATIONS WERE TAKEN: WITH
LEVEL SET UP NEAR A, OBSERVED READINGS ARE A=1.855M AND B=1.434M; WITH LEVEL SET UP NEAR B, C= 1.790M AND
D=2.211M. DETERMINE THE CORRECT READING ON THE ROD HELD AT A WITH THE INSTRUMENT STILL IN THE SAME
POSITION AT B FOR A HORIZONTAL LINE OF SIGHT.
2.
TWO PEG TEST. THE TWO-PEG TEST IS USED TO DETERMINE IF THE LINE OF SIGHT OF THE TELESCOPE IS PARALLEL
TO THE AXIS OF THE BUBBLE TUBE. A TILTING LEVEL IS SET UP HALFWAY BETWEEN POINTS A AND B AND ROD READINGS ON
BOTH POINTS ARE 1.969M AND 2.161 M, RESPECTIVELY. THE LEVEL IS THEN SET UP 1.50M AWAY FROM A ALONG THE
EXTENSION OF THE LINE AB AND 53.50 FROM B. THEN ROD READINGS ON A AND B WERE RECORDED AS 1.554M AND
1.728M, RESPECTIVELY. DETERMINE IF THE LINE OF SIGHT IS INCLINED DOWNWARD OR UPWARD AND THE AMOUNT BY
WHICH THE HORIZONTAL CROSS HAIR SHOULD BE MOVED TO ADJUST THE LINE OF SIGHT.
3.
DIFFERENCE IN ELEVATION. A DUMPY LEVEL IS SET UP AND LEVELED APPROXIMATELY HALFWAY BETWEEN TWO
POINTS, C AND D. THE ELEVATION OF POINT C IS 135.00M ABOVE THE MAIN SEA LEVEL AND THE READING ON A ROD HELD
AT THIS POINT IS 1.52M. IF THE READING ON THE ROD HELD AT POINT D IS 2.74 M, DETERMINE THE DIFFERENCE IN
ELEVATION BETWEEN THE TWO POINTS. ALSO, DETERMINE THE ELEVATION AT POINT D.
4.
DIFFERENCE IN ELEVATION. THE BACKSIGHT READING ON A POINT IS 2.25 M AND THE FORESIGHT READING ON A
SECOND POINT IS 0.86 M. IF THE ELEVATION OF THE FIRST POINT IS 460.96 M, DETERMINE THE ELEVATION OF THE
SECOND POINT.
5.
DIFFERENCE IN ELEVATION. READING ON A ROD HELD AT TWO POINT A AND B, 75 M APART, ARE 2.965 M AND
1.215M, RESPECTIVELY. DETERMINE THE ROD READING AT POINTS ON LINE AB WHICH ARE 25 M AND 45 M FROM A.
ASSUME THAT THERE IS A UNIFORM GRADIENT ALONG LINE AB.
6.
CURVATURE AND REFRACTION. DETERMINE THE COMBINED EFFECT OF CURVATURE AND REFRACTION ON LEVEL
SIGHTS OF 30, 50, 100, 250, 300, 500, 1000 AND 2000 M.
7.
CURVATURE AND REFRACTION. A BACKSIGHT OF 3.055M IS TAKEN ON A POINT 75M FROM A LEVEL STATION AND
FORESIGHT OF 1.258M FROM THE SAME STATION. DETERMINE THE DIFFERENCE IN ELEVATION BETWEEN THE TWO POINTS,
TAKING INTO ACCOUNT THE COMBINED EFFECT OF CURVATURE AND REFRACTION.
8.
CURVATURE AND REFRACTION. DETERMINE THE BACKSIGHT OR FORESIGHT DISTANCE FOR AN INSTRUMENT SET UP
WHICH WILL CAUSE AN ERROR DUE TO THE EARTH’S CURVATURE AND ATMOSPHERIC REFRACTION EQUAL TO 0.0015M,
0.0575 M, 0.0986M, 0.2935 M, AND 0.8750M.
9.
CURVATURE AND REFRACTION. AN OBSERVER STANDING ON SHORE CAN JUST SEE THE TOP OF A LIGHTHOUSE
16.5 KM AWAY. IF THE EYE HEIGHT OF THE OBSERVER ABOVE SEA LEVEL IS 1.735M, DETERMINE THE HEIGHT OF THE
LIGHTHOUSE ABOVE SEA LEVEL. NEGLECT THE EFFECT OF THE WAVES.
10.
CURVATURE AND REFRACTION. DETERMINE HOW FAR ( IN KM ) OUT FROM SHORE AN INTER- ISLAND VESSEL WILL
BE WHEN A RED LIGHT ON ITS DECK, 9.45 M ABOVE THE WATER, DISAPPEARS FROM THE LINE OF SIGHT OF A CHILD
STANDING ON SHORE AND WHOSE EYE LEVEL IS 1.32 M ABOVE THE WATER.
11.
CURVATURE AND REFRACTION. BY TAKING A SIGHT ACROSS A LAKE 24 KM WIDE THROUGH A PAIR OF
BINOCULARS, DETERMINE THE HEIGHT OF THE SHORTEST TREE ON THE OPPOSITE SHORE WHOSE TIP THE OBSERVER CAN
SEE. ASSUME THAT THE EYES OF THE OBSERVER ARE 1.675 M ABOVE THE SHORE LINE ON WHICH HE STANDS.
12.
CURVATURE AND REFRACTION. TWO TOWERS, A AND B, ARE LOCATED ON LEVEL GROUND AND THEIR BASES HAVE
EQUAL ELEVATIONS ABOVE SEA LEVEL. DETERMINE THE DISTANCE BETWEEN THE TWO TOWERS IF A PERSON STANDING ON
TOP OF TOWER A CAN JUST SEE THE TOP OF TOWER B. HIS EYES ARE 15.50 M ABOVE THE GROUND.
13.
CURVATURE AND REFRACTION. A LIFEGUARD IS STANDING ON A WATCHTOWER AT THE EDGE OF THE WATER
SUCH THAT HIS EYE LEVEL IS 3.50 M ABOVE SEA LEVEL. IF A LIFE RAFT STARS FLOATING OUT TO SEA, DETERMINE HOW FAR
OUT IT COULD GO BEFORE IT DISAPPEARS FROM THE SIGHT OF THE LIFEGUARD. ASSUME THAT THE SEA IS CALM AND A PAIR
OF BINOCULARS IS AVAILABLE TO TRACT THE MOVEMENT OF THE RAFT.